#include "cs.h"
/* [L,U,pinv]=lu(A, [q lnz unz]). lnz and unz can be guess */
csn *cs_lu (const cs *A, const css *S, double tol)
{
    cs *L, *U ;
    csn *N ;
    double pivot, *Lx, *Ux, *x,  a, t ;
    int *Lp, *Li, *Up, *Ui, *pinv, *xi, *q, n, ipiv, k, top, p, i, col, lnz,unz;
    if (!CS_CSC (A) || !S) return (NULL) ;	    /* check inputs */
    n = A->n ;
    q = S->q ; lnz = S->lnz ; unz = S->unz ;
    x = cs_malloc (n, sizeof (double)) ;	    /* get double workspace */
    xi = cs_malloc (2*n, sizeof (int)) ;	    /* get int workspace */
    N = cs_calloc (1, sizeof (csn)) ;		    /* allocate result */
    if (!x || !xi || !N) return (cs_ndone (N, NULL, xi, x, 0)) ;
    N->L = L = cs_spalloc (n, n, lnz, 1, 0) ;	    /* allocate result L */
    N->U = U = cs_spalloc (n, n, unz, 1, 0) ;	    /* allocate result U */
    N->pinv = pinv = cs_malloc (n, sizeof (int)) ;  /* allocate result pinv */
    if (!L || !U || !pinv) return (cs_ndone (N, NULL, xi, x, 0)) ;
    Lp = L->p ; Up = U->p ;
    for (i = 0 ; i < n ; i++) x [i] = 0 ;	    /* clear workspace */
    for (i = 0 ; i < n ; i++) pinv [i] = -1 ;	    /* no rows pivotal yet */
    for (k = 0 ; k <= n ; k++) Lp [k] = 0 ;	    /* no cols of L yet */
    lnz = unz = 0 ;
    for (k = 0 ; k < n ; k++)	    /* compute L(:,k) and U(:,k) */
    {
	/* --- Triangular solve --------------------------------------------- */
	Lp [k] = lnz ;		    /* L(:,k) starts here */
	Up [k] = unz ;		    /* U(:,k) starts here */
	if ((lnz + n > L->nzmax && !cs_sprealloc (L, 2*L->nzmax + n)) ||
	    (unz + n > U->nzmax && !cs_sprealloc (U, 2*U->nzmax + n)))
	{
	    return (cs_ndone (N, NULL, xi, x, 0)) ;
	}
	Li = L->i ; Lx = L->x ; Ui = U->i ; Ux = U->x ;
	col = q ? (q [k]) : k ;
	top = cs_spsolve (L, A, col, xi, x, pinv, 1) ;	/* x = L\A(:,col) */
	/* --- Find pivot --------------------------------------------------- */
	ipiv = -1 ;
	a = -1 ;
	for (p = top ; p < n ; p++)
	{
	    i = xi [p] ;	    /* x(i) is nonzero */
	    if (pinv [i] < 0)	    /* row i is not yet pivotal */
	    {
		if ((t = fabs (x [i])) > a)
		{
		    a = t ;	    /* largest pivot candidate so far */
		    ipiv = i ;
		}
	    }
	    else		    /* x(i) is the entry U(pinv[i],k) */
	    {
		Ui [unz] = pinv [i] ;
		Ux [unz++] = x [i] ;
	    }
	}
	if (ipiv == -1 || a <= 0) return (cs_ndone (N, NULL, xi, x, 0)) ;
	if (pinv [col] < 0 && fabs (x [col]) >= a*tol) ipiv = col ;
	/* --- Divide by pivot ---------------------------------------------- */
	pivot = x [ipiv] ;	    /* the chosen pivot */
	Ui [unz] = k ;		    /* last entry in U(:,k) is U(k,k) */
	Ux [unz++] = pivot ;
	pinv [ipiv] = k ;	    /* ipiv is the kth pivot row */
	Li [lnz] = ipiv ;	    /* first entry in L(:,k) is L(k,k) = 1 */
	Lx [lnz++] = 1 ;
	for (p = top ; p < n ; p++) /* L(k+1:n,k) = x / pivot */
	{
	    i = xi [p] ;
	    if (pinv [i] < 0)	    /* x(i) is an entry in L(:,k) */
	    {
		Li [lnz] = i ;	    /* save unpermuted row in L */
		Lx [lnz++] = x [i] / pivot ;	/* scale pivot column */
	    }
	    x [i] = 0 ;		    /* x [0..n-1] = 0 for next k */
	}
    }
    /* --- Finalize L and U ------------------------------------------------- */
    Lp [n] = lnz ;
    Up [n] = unz ;
    Li = L->i ;			    /* fix row indices of L for final pinv */
    for (p = 0 ; p < lnz ; p++) Li [p] = pinv [Li [p]] ;
    cs_sprealloc (L, 0) ;	    /* remove extra space from L and U */
    cs_sprealloc (U, 0) ;
    return (cs_ndone (N, NULL, xi, x, 1)) ;	/* success */
}
